Other options:
There's one of the burger chains just across the road next to the Shell
filling station (out of the hotel, turn left, and cross Bath Road at the
junction). I'd say which one (i.e McDonalds, Burger King, etc) but even
though I drive past it a couple of times a day, a couple of days per week
most weeks, I don't actually remember.
I think there are a few options along Bath Road itself as well. Probably
all on the other side of the road. (Or, just remembered, there's the Arnos
Vale Cafe - out of the hotel, turn left and walk along Bath Road, and it
should be signposted from the entrance to the Arnos Vale Cemetery - no
crossing of roads).
Slightly further afield (I should think maybe 1 to 1.5 KM) there's Avon
Meads Shopping Park where there's another chain burger outlet (again, not
sure offhand which one), and a Krispy Kreme drive through. Not the
healthiest of things to eat but, you know, doughnuts. ;)